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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
341 lines
12 KiB
C#
341 lines
12 KiB
C#
// Accord Statistics Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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namespace Accord.Statistics.Distributions.Univariate
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{
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using System;
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using Accord.Statistics.Testing;
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using Accord.Math;
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using Accord.Compat;
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/// <summary>
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/// Shapiro-Wilk distribution.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// The Shapiro-Wilk distribution models the distribution of <see cref="ShapiroWilkTest">
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/// Shapiro-Wilk's</see> <see cref="IHypothesisTest">test statistic</see>. </para>
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///
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///
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/// <para>
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/// References:
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/// <list type="bullet">
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/// <item><description><a href="http://sci2s.ugr.es/keel/pdf/algorithm/articulo/royston1982.pdf">
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/// Royston, P. "Algorithm AS 181: The W test for Normality", Applied Statistics (1982),
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/// Vol. 31, pp. 176–180. </a></description></item>
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/// <item><description><a href="http://lib.stat.cmu.edu/apstat/R94">
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/// Royston, P. "Remark AS R94", Applied Statistics (1995), Vol. 44, No. 4, pp. 547-551.
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/// Available at http://lib.stat.cmu.edu/apstat/R94 </a></description></item>
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/// <item><description>
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/// Royston, P. "Approximating the Shapiro-Wilk W-test for non-normality",
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/// Statistics and Computing (1992), Vol. 2, pp. 117-119. </description></item>
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/// <item><description>
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/// Royston, P. "An Extension of Shapiro and Wilk's W Test for Normality to Large
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/// Samples", Journal of the Royal Statistical Society Series C (1982a), Vol. 31,
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/// No. 2, pp. 115-124. </description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a new Shapiro-Wilk's W for 5 samples
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/// var sw = new ShapiroWilkDistribution(samples: 5);
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///
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/// double mean = sw.Mean; // 0.81248567196628929
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/// double median = sw.Median; // 0.81248567196628929
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/// double mode = sw.Mode; // 0.81248567196628929
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///
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/// double cdf = sw.DistributionFunction(x: 0.84); // 0.83507812080728383
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/// double pdf = sw.ProbabilityDensityFunction(x: 0.84); // 0.82021062372326459
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/// double lpdf = sw.LogProbabilityDensityFunction(x: 0.84); // -0.1981941135071546
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///
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/// double ccdf = sw.ComplementaryDistributionFunction(x: 0.84); // 0.16492187919271617
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/// double icdf = sw.InverseDistributionFunction(p: cdf); // 0.84000000194587177
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///
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/// double hf = sw.HazardFunction(x: 0.84); // 4.9733281462602292
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/// double chf = sw.CumulativeHazardFunction(x: 0.84); // 1.8022833766369502
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///
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/// string str = sw.ToString(CultureInfo.InvariantCulture); // W(x; n = 12)
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/// </code>
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/// </example>
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///
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[Serializable]
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public class ShapiroWilkDistribution : UnivariateContinuousDistribution, IFormattable
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{
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Func<double, double> g; // forward transformation
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Func<double, double> h; // inverse transformation
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NormalDistribution normal;
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/// <summary>
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/// Gets the number of samples distribution parameter.
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/// </summary>
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///
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public int NumberOfSamples { get; private set; }
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/// <summary>
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/// Creates a new Shapiro-Wilk distribution.
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/// </summary>
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///
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/// <param name="samples">The number of samples.</param>
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///
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public ShapiroWilkDistribution([PositiveInteger(minimum: 4)] int samples)
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{
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if (samples < 4)
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{
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throw new ArgumentOutOfRangeException("samples",
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"The number of samples must be higher than 3.");
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}
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this.NumberOfSamples = samples;
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if (samples <= 11)
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{
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double n = samples;
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double n2 = n * n;
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double n3 = n2 * n;
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double alpha = 0.459 * n - 2.273;
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this.g = w => -Math.Log(alpha - Special.Log1m(w));
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this.h = w => Math.Exp(-Math.Exp(-alpha)) * (Math.Exp(Math.Exp(-alpha)) - Math.Exp(w));
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double mean = -0.0006714 * n3 + 0.0250540 * n2 - 0.39978 * n + 0.54400;
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double sigma = Math.Exp(-0.0020322 * n3 + 0.0627670 * n2 - 0.77857 * n + 1.38220);
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this.normal = new NormalDistribution(mean, sigma);
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}
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else
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{
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double u = Math.Log(samples);
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double u2 = u * u;
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double u3 = u2 * u;
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this.g = w => Special.Log1m(w);
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this.h = w => 1 - Math.Exp(w);
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double mean = 0.00389150 * u3 - 0.083751 * u2 - 0.31082 * u - 1.5861;
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double sigma = Math.Exp(0.00303020 * u2 - 0.082676 * u - 0.48030);
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this.normal = new NormalDistribution(mean, sigma);
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}
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}
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/// <summary>
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/// Gets the support interval for this distribution.
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/// </summary>
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///
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/// <value>
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/// A <see cref="DoubleRange" /> containing
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/// the support interval for this distribution.
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/// </value>
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///
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public override DoubleRange Support
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{
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get { return new DoubleRange(0, 1); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the mean for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's mean value.
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/// </value>
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///
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public override double Mean
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{
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get { return h(normal.Mean); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the mode for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's mode value.
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/// </value>
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///
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public override double Mode
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{
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get { return h(normal.Mode); }
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set { } //Not Implemented.
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Variance
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{
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get { throw new NotSupportedException(); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the median for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's median value.
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/// </value>
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///
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public override double Median
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{
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get { return h(normal.Median); }
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Entropy
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{
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get { throw new NotSupportedException(); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the cumulative distribution function (cdf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="x">A single point in the distribution range.</param>
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///
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/// <remarks>
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/// The Cumulative Distribution Function (CDF) describes the cumulative
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/// probability that a given value or any value smaller than it will occur.
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/// </remarks>
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///
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/// <example>
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/// See <see cref="ShapiroWilkDistribution"/>.
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/// </example>
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///
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protected internal override double InnerDistributionFunction(double x)
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{
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double z = g(x);
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double cdf = normal.ComplementaryDistributionFunction(z);
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return cdf;
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}
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/// <summary>
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/// Gets the complementary cumulative distribution function
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/// (ccdf) for this distribution evaluated at point <c>x</c>.
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/// This function is also known as the Survival function.
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/// </summary>
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///
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/// <param name="x">A single point in the distribution range.</param>
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///
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/// <remarks>
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/// The Complementary Cumulative Distribution Function (CCDF) is
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/// the complement of the Cumulative Distribution Function, or 1
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/// minus the CDF.
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/// </remarks>
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///
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protected internal override double InnerComplementaryDistributionFunction(double x)
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{
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double z = g(x);
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return normal.DistributionFunction(z);
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}
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/// <summary>
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/// Gets the probability density function (pdf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="x">A single point in the distribution range.</param>
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///
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/// <returns>
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/// The probability of <c>x</c> occurring
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/// in the current distribution.
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/// </returns>
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///
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/// <remarks>
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/// The Probability Density Function (PDF) describes the
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/// probability that a given value <c>x</c> will occur.
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/// </remarks>
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///
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protected internal override double InnerProbabilityDensityFunction(double x)
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{
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double z = g(x);
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return normal.ProbabilityDensityFunction(z);
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}
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/// <summary>
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/// Gets the log-probability density function (pdf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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/// <param name="x">A single point in the distribution range.</param>
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/// <returns>The logarithm of the probability of <c>x</c>
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/// occurring in the current distribution.</returns>
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/// <remarks>The Probability Density Function (PDF) describes the
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/// probability that a given value <c>x</c> will occur.</remarks>
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protected internal override double InnerLogProbabilityDensityFunction(double x)
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{
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double z = g(x);
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return normal.LogProbabilityDensityFunction(z);
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override void Fit(double[] observations, double[] weights, Fitting.IFittingOptions options)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Creates a new object that is a copy of the current instance.
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/// </summary>
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/// <returns>
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/// A new object that is a copy of this instance.
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/// </returns>
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///
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public override object Clone()
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{
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return new ShapiroWilkDistribution(NumberOfSamples);
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}
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/// <summary>
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/// Returns a <see cref="System.String"/> that represents this instance.
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/// </summary>
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///
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/// <returns>
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/// A <see cref="System.String"/> that represents this instance.
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/// </returns>
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///
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public override string ToString(string format, IFormatProvider formatProvider)
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{
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return String.Format("W(x; n = {0})",
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NumberOfSamples.ToString(format, formatProvider));
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}
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}
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} |